Question

Consider the functions f and g in the tables below. f(x) = 90x2 + 180x + 92 x y 0 92 1 362 2 812 3 1,442 4 2,252 5 3,242 g(x) = 6x x y 0 1 1 6 2 36 3 216 4 1,296 5 7,776 Which of the following statements is true? At approximately x = 4.39, the rate of change of f is equal to the rate of change of g. For every value of x, the rate of change of g exceeds the rate of change of f. As x increases, the rate of change of f exceeds the rate of change of g. As x increases, the rate of change of g exceeds the rate of change of f.
PLS HELP ASAP

Answer 1

Since f(x) is a polynomial function and g(x) is an exponential function, we know that both the value and the rate of change of g(x) will exceed those of f(x) when x gets large.

The rate of change of g(x) is less than that of f(x) for x < 3.4. The value of g(x) is less than that of f(x) for x < 4.39. Of the statements offered, the only one that is true is ...

... As x increases, the rate of change of g exceeds the rate of change of f.

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In the attached graph, the functions are graphed as solid lines; their rates of change are graphed as dashed lines of the same color.